Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions | Zendy

Michael Field | Zendy; Ian Melbourne | Zendy; Andrew Török | Zendy

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Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions

Author(s) -

Michael Field,

Ian Melbourne,

Andrew Török

Publication year - 2003

Publication title -

ergodic theory and dynamical systems

Language(s) - English

Resource type - Journals

eISSN - 1469-4417

pISSN - 0143-3857

DOI - 10.1017/s0143385702000901

Subject(s) - mathematics , equivariant map , central limit theorem , brownian motion , lie group , limit (mathematics) , fractional brownian motion , exponential function , pure mathematics , group (periodic table) , transfer (computing) , motion (physics) , brownian excursion , mathematical analysis , transfer operator , mathematical physics , geometric brownian motion , classical mechanics , physics , quantum mechanics , diffusion process , knowledge management , computer science , statistics , innovation diffusion , parallel computing

H ¨ older continuous observations on hyperbolic basic sets satisfy strong statistical properties such as exponential decay of correlations, central limit theorems and invariance principles (approximation by Brownian motion). Using an equivariant version of the Ruelle transfer operator studied by Parry and Pollicott, we obtain similar results for equivariant observations on compact group extensions of hyperbolic basic sets.

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